The effective Young's modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20-684 nm by measuring resonance frequencies from thermal noise spectra. A significant deviation from the bulk value is observed for cantilevers thinner than 150 nm. To explain the observations we have compared the thickness dependence of the effective Young's modulus for the first and second flexural resonance mode and measured the static curvature profiles of the cantilevers. We conclude that surface stress cannot explain the observed behavior. A surface elasticity model fits the experimental data consistently. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3152772͔ Micro-and nanoelectromechanical systems are widely studied for their application in sensing and actuation devices. 1 Down-scaling of such devices improves their sensitivity however at the same time mechanical properties may start to deviate from the bulk behavior. The finite-size effects have been the subject of theoretical studies for the past years. [2][3][4][5][6][7][8] In experimental work on single-crystalline Si cantilevers it has been shown that the Young's modulus strongly depends on the thickness. 9 This behavior has also been observed for suspended crystalline silver nanowires. 10 In describing the properties of nanoscale devices, the bulk Young's modulus ͑E͒ is generally replaced by the effective Young's modulus ͑E eff ͒ to account for size-dependent effects, including surface stress. The total surface stress ͑⌺͒ can be written as a sum of a strain-independent part ͑ ͒ and a strain-dependent part ͑strain ⑀͒, which is related to surface elasticity ͑C s ͒ ⌺ = + C s ⑀. [11][12][13][14][15] In this letter, we study the size-dependency of the Young's modulus in silicon nitride cantilevers when one dimension ͑cantilever thickness͒ is scaled down from 684 to 20 nm. As the SiN x is amorphous, it is difficult to distinguish between the two contributions since parameters ͑e.g., C s ͒ are unknown and difficult to calculate. However, by comparing the experimental data for the first and second mode to theory, we show that the straindependent part of the total surface stress is responsible for the size-dependency.Cantilevers are fabricated from low-pressure chemical vapor deposited ͑LPCVD͒ silicon nitride ͑SiN x ͒ on Si͑100͒ substrates and are patterned with an electron-beam pattern generator. After resist development we use reactive ion etching in a CHF 3 / O 2 ͑20:1͒ plasma to transfer the pattern to the SiN x layer. After this step cantilevers are released using a KOH etch process ͑15 min etching time at 85°C; Si etch rate about 1 m / min͒, yielding facetting along the ͑111͒ planes, as shown in Fig. 1͑a͒. This process introduces a negligible undercut, so that length corrections can be disregarded. 16 Cantilevers are fabricated with the following dimensions: lengths ͑L͒ from 8 to 100 m, widths ͑w͒ 8, 12, or 17 m, and thicknesses ͑h͒ ranging from 20 to 684 nm.The thickness was measured using an ellipsometer ͑Leitz SP͒ with an accuracy of ...
We present a systematic investigation of the dynamic properties of silicon nitride cantilevers in air. The thermal noise spectra of cantilevers have been measured using a home-made optical deflection setup. Torsional and flexural resonances up to the seventh mode are observed. The dependence of resonance frequencies on the dimensions and mode number is studied in detail. It is found that undercut increases the effective length of the cantilever by a value L, which depends on the undercut distance and the resonance mode shape, but not on the cantilever length. Finite element modelling confirms these experimental findings. A simple model is suggested for the shape of the undercut region, which agrees well with experimental findings. Using this model, the undercut cantilever can be approximated by a stepped beam, where the clamp distance depends on the underetch duration and the mode shape.
We have developed a sensor to study the mechanical stiffness of atomic-size contacts. It consists of a modification of the mechanically controllable break-junction technique, using a quartz tuning fork resonator as force sensor. We present first results of measurements of the force constants in gold atomic contacts. In the formation of chains of single-metal atoms, the folding in of individual atoms from the banks into the chain can be observed. This sensor allows one to measure forces in atomic contacts for a wide variety of metals, as illustrated with the first measurements on platinum.
Micro/nano resonant cantilevers with a laser deflection readout have been very popular in sensing applications over the past years. Despite the popularity, however, most of the research has been devoted to increasing the sensitivity, and very little attention has been focused on effects-induced errors. Among these effects, the surface effects and the so-called readout back-action are the two most influential causes of errors. In this paper, we investigate (1) the influence of the surface effects such as water adsorption, gas adsorption, and generally surface contaminations, and (2) the effect of the laser deflection detection, including power and positions of the laser, on the resonance frequency of silicon cantilevers. Our results show that both the surface contaminations and the laser back-action effects can significantly change the resonant response of the cantilevers. We conclude that the effects have to be taken into account, particularly in the case of ultra high sensitivity cantilevers.
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